Fast Simulation of Logging-While-Drilling Resistivity Measurement Tool With Multiple Circular Antenna Recesses Using a Semianalytical Finite-Element Method

The technology of logging-while-drilling (LWD) resistivity measurement, which derives formation resistivity from multiple transmitter–receiver antenna configurations, has been widely applied in geosteering and reservoir evaluation. The LWD sensors are typically mounted on grooved metal mandrels, with the antenna recesses filled with ferrite or other magnetic materials. This study employs a semianalytical finite-element method (SAFEM) in cylindrical coordinates for fast and accurate simulation of LWD tool responses in a layered medium with multiple antenna grooves. This method discretizes only the cross sections of the stratified structure and derives high-accuracy analytical formulations in each piecewise-homogeneous layer, thereby eliminating the need for longitudinal meshing. By transforming a 3-D problem into a 2-D axisymmetric one in a cylindrical coordinate system and then into a series of 1-D problems, the proposed SAFEM significantly reduces computational cost while maintaining accuracy comparable to the conventional finite-element (FE) method. To validate the accuracy and efficiency of the proposed SAFEM scheme, we compare the numerical results with COMSOL for homogeneous formations. Furthermore, the response characteristics of different transmitter–receiver antenna pairs are investigated, and the effects of antenna recess structures on LWD tool responses are analyzed through numerical experiments. Finally, a 28-layer Oklahoma model with invaded formations is simulated to evaluate the detection performance of different antenna configurations.